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Research Strategy and Strategic Options
for Mathematics Departments
Peter Grindrod CBE
Mathematical Institute
University of Oxford
June 3, 2021
Abstract
Very rarely do I ever seek to influence academic colleagues. My normal concerns reflect the interests of
the sectors which my own research and active collaborations seek to serve (my own selfish spheres of interest),
in terms of strategy, leadership and rather specific research goals, for a variety of national institutions, public
and commercial actors. Mathematics is sometimes supportable, inspirational, enabling, game-changing. and
visionary (in parts) and also sometimes vulnerable, misunderstood, and mistreated (in parts). Recent events
have led me to think that an almost wilful avoidance of research strategy within the mathematics community
is now causing our discipline some real harm. And some non-repairable harm. Mathematics is like a “candle
in the wind". This work is a repost, and a call to all departments of mathematics everywhere (but especially
in the UK) to produce forceful and actionable research and innovation strategies as a form of defence and as
a form of advancement for aspirational and progressive valuable research activities.
I believe that others within the ecosystem will respond in kind to us, but we must first engage properly. Here
are some practical thoughts about the “why", “how", and “what" of research strategy for mathematics departments
in 2021. I offer this for discussion only because I care deeply about what will happen to us in the future.
Here we discuss a variety of issues, including the relationship between fundamental mathematics and
disruptive, often unforeseen, applications in the future, responding to and succeeding in the face of future
unknown unknowns in a way that that the nation has a right to expect. In ways that the government desires.
We discuss some consequences for universities that ignore this.
We discuss a range of options for strategic research policies that may be useful to UK mathematics de-
partments in forming their own research strategies and contributing to the research strategies of larger units
within their host universities.
1 What is the use of strategy?
Why do university mathematics departments need to have a research strategy? As we shall see a strategy
gives both an overall approach to navigating the challenges and opportunities, whilst it also provides a solid
foothold to rely on, and can brace the department against external forces. A department without a strategy
is a “candle in the wind". It is often at the mercy or others’ strategies and cannot assert hard non-negotiable
priorities, or articulate any hard consequences and risks (theats).
In a changing world, governments, regulators, funders, and universities themselves have their own strate-
gies (to varying extents) and reviews and changes to these are expected to effect changes within their own
domains. And such changes may result in discontinuities (with both positive and negative implications) for
mathematics departments.
Of course mathematics itself is a unique subject. The certainties of proof and truth leave no room for
subjective argument, though conjectures and opinions are useful spurs. In the end, truth is demonstrably
there or it isn’t. A school student can enjoy the certainty of success in achieving through exercises and most
examination candidates leave the room with a good idea of the marks that they have achieved, by imagin-
ing the marks available for their relatively successful answers (“hence or otherwise show that..."). Recently
though, this last “unique correct answer" property (of well-defined problems) has led to allegations of the
racist perpetuation of historical white advantage. That issue is for another day, but it again exemplifies the
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Grindrod - Research Strategy for Mathematics Departments
uniqueness of mathematical endeavours – we cannot have a meaningful mathematics trading subjectives
truths from alternative viewpoints. It is one mathematics for all. So, rather than change the nature of math-
ematics itself, we do have to make it far more inclusive. That might be a strategic policy aim by the way (see
next section).
Mathematical research is also gloriously unpredictable, moving ahead in both small steps and large leaps.
And hardly something that requires strategy, other than allowing individuals to commit to selected reasonable
lines of attack. In short the internal working of mathematics require little strategy and progress (and success)
is rarely governable by having best laid plans.
These days the problems inherent in a “strategy vacuum" affect the departmental body, rather than in-
dividual members of the academic mathematics community. This is because it is visible, or not, at the in-
terfaces: the interfaces between mathematics and other subjects (science and technology, social science,
medical science, arts culture and humanities); and the interfaces between mathematics departments and
their host institutions (academic divisions, and senior management functions). These are two-way streets,
and we argue that there are real risks in not engaging at a strategic level, and asserting our own aspirations,
goals and red lines.
We will see that the advantages of a clear and commonly articulated strategy are both practical (trans-
actional), in both advancing departmental activities and in asserting priorities; and motivational (and thus
an enabling feature of true leadership). While the risks inherent in having weak or vacuous strategy can be
existential for departments, in whole or in part.
We must deal with external forces by engaging with their own strategies and objectives, like wrestling
an octopus. In those terms a strong and certain foothold will be an advantage, to push against – we only
need to be a lap ahead, rather than playing catch-up with externally imposed agendas.
2 What is a strategy?
For our purposes here we will follow Rumelt [1], since we need a definition.
A strategy consists of three things.
•A Diagnosis. This is a response to the question “What is going on?", and applies both to externally
generated forces (and constraints), and internally, within the subject or the academic body. A good
diagnosis must be reviewed regularly and act as a list of potential challenges and opportunities. It
describes the world in which we must strive, survive, and thrive.
•A Policy. This is an overall set of statements about how will will act, organise and and progress, and
might include some commitments, some objectives (that measurable and hopefully be widely sup-
ported), and some priorities (which are sometimes divisive) .
•Some consequent actions. This is a list of things to be achieved in progressing the policy within the
external situations (the diagnosis). These may be diverse but they will contribute to the whole.
Parts of any strategy are clearly inward-facing, allowing department members to have transparency and
see how their own separate contributions will accumulate to achieve the greater progress of the whole
policy. Parts of the strategy are clearly outward-facing. We are giving others (often those set above us) hard
assurances that we have matters in hand and that appropriate responses to their own policies and concerns
will be delivered.
This is especially important when host universities impose their own strategies onto mathematics depart-
ments, or treat the mathematics departments in a way that is disadvantageous. For example many mathemat-
ics departments are relatively well-run financially, since they require relatively little in capital investment,
their main costs are in heads, and departments have consistent income from T&L; whereas as other science
departments often represent year-on-year black holes for budget. Quite typically internal monies may be
channelled to fill-in the holes (leaving mathematics alone) or else necessary cuts are spread out across all
departments regardless of where the losses are made. We have all seen this, and quite often the Dean or
PVC sees it as their role to socialise this spreading out of the corporate pain (itself showing their own lack
of strategy or even priorities). In our view cuts should be imposed where losses are made. We recall one
such case where a mathematics department was asked to take pro-rata cuts being applied across the science
faculty, and feel good about general, multidisciplinary, and thematic appointments to be made elsewhere.
The point is that without a strategy a mathematics department cannot inform those external actors about
the costs and consequences of imposing changes blindly from outside. They cannot show what will go: and
the default is that mathematics departments will manage the change and “suck it up". A strategy would point
to the potential for risk and real damage.
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Once research capabilities or teams are lost they may take decades to restore, if ever. Mathematics is a
long-term game and its currency is “excellence". Timescales are very important. They are not the same within
all fields. In data science and AI, for example, things move at a much faster pace with algorithms leaving
the “lab" and becoming exploited within days and months. Fundamental mathematics is very different in
terms of delivery and impact. Huge paradigm changes are possible when progress is made and we can
all enter another room, one previously locked or even unknown to us. The power of mathematical ideas to
transport us into new fields of knowledge is what we should call “true innovation”. For the past two decades
the UK’s research councils and public funding sector has hijacked the word “innovation" and redefined it
as“multidisciplinary and impactful" (and possibly with defined stakeholders too): this is to deny the existence
of game-changing and fundamental innovations within a single discipline, and especially with mathematics,
where the rigour guarantees one-time changes. Seemingly unbeknown to the powers that be, mathematics
in the UK is especially excellent internationally and this foundation is a reliable and true asset for the nation
and our universities.
Here we come to our first difficulty. Even having a strategy is an anathema for some colleagues (at
least until they day they realise it would have been useful). This is because most mathematicians have not
succeeded, or perceived that they have succeeded, through the existence of abstract and executive strategies.
But they may find themselves the beneficiaries of some such, yet see this as just reward for achievements at
best, or as luck at worst. We should change culture and see department strategy as a shield and a weapon, or
tool, with which to drive internal improvements and to engage with external impositions and opportunities.
Returning to the general definition of a strategy (given above), what a strategy is not is a long list of
name-checks for bundles of activities and past achievements. This often occurs when strategies are formed
by committees: we refer to this as the “peril of inclusivity". It is quite common within universities’ central
management. It is particular prevalent at the university institutional level. Nevertheless, these days they
often contain clear commitments (that are “policies") and specific priorities, especially in response pressure
from national needs. and requirements.
Equally a strategy is not a cultural account of the indivisibility of mathematics, referring to the many and
varied connected threads running from the rigorous foundations and standards of fundamental mathematics
into applications (and indeed those rights of passage), and the development of common vocabularies, con-
cepts, methods, and understandings. While we have huge enthusiasm for this, for example when posting
“one cannot harvest extraordinary fruit from a tree’s branches without also caring for the roots”, such a nar-
rative is often seen as special pleading from outside (see section 4). A strategy may only rely on this type of
consensus (self-evident truths) internally. And it has to be effective externally for generalists.
We used to have a boss who often said, “If it ain’t broke, then don’t mend it". Many mathematicians
may take this view. The problem with this is that strategies may become obsolete within a new diagnosis.
One cannot hold on to the past when the external environments become more future-orientated. Of course,
doing nothing is also a possible strategy. There have been moments in many institutions’ histories where
the correct thing was to do nothing and wait for external things (beyond their control) to reorganise: but this
is never a permanent state of affairs. Doing nothing now means being ready to act with clarity and agility
when things begin to change (and not after they have changed).
It is often said that the “the best form of defence is attack and the most vital element of attack is surprise".
A proactive strategy for a mathematics department will indeed take many senior managers within our own
institutions somewhat by surprise, and the purpose of this work is to encourage all mathematics departments
to develop such a strategy, even including working together across the nation, and to examine some useful
options for consideration.
Senior management within institutions are basically trying to align themselves with the national actors
(Research England, UKRI, and the Office for Students, for example). They are thus wary of being out of step
with national emerging initiatives – there is risk in that and potential blame for themselves. These days
new initiatives are coming rather thick and fast and almost everything in the T&L and R&D ecosystems is
changing. Global influence and success is highly prized by the government and every university seeks to
prosper. Universities are very cautious about criticising fast-moving governmental and national initiatives
(reorganisations of oversight and funding, and new actors such as the up-coming ARIA), for fear of being
placed on the naughty step. This lack of any assertive presence plays into the hands of further government
and national strategies. Universities rarely point-up risks or discuss bad consequences of proposed changes
(within public consultations, etc).
Against this background the mathematics department should assert the future value, and the potential
advantages to be gained, from mathematical excellence, and produce some bullets that the university will
fire itself. Once one sees the host university adopt the vocabulary of mathematics strategy within their own
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publicly stated strategies, one will know that mathematics is winning. That should be the only test.
3 Horses for courses
Not all mathematics departments are of a size that they can assert their own strategies. They may be con-
sidered as a part of a number of smallish departments within the Science Faculty. In that case they have to
make a proactive contribution to the development of strategy for the unit.
Other mathematics departments , including those in the top fifty worldwide, are certainly in a position to
create their own strategies, being usually allowed to mostly run their own show, though subject to constraints
in spending (by which we mean spending their own resources).
So strategy must be enabling in different ways depending upon how the department is managed within
the overall university structure. In both cases the option of having no discernible strategy is very high risk
though.
To summarise, we need to develop global strategies for our largest departments. We need to develop
common cause for small departments across units within their own institutions: perhaps a strategy for the
faculty of science or the sub-faculty. The irony is that mathematicians have the skills that could make very
valuables contributions to these. So we have to become proactive and present options: being on the front
foot as opposed to the back foot.
4 The balance between fundamental mathematics and applications
We have previously touched on a particular strategic issue for mathematics which occurs when a university
seeks to re-balance or re-shape its departments and consequently seeks to diminish effort and resources
within fundamental mathematics in order to grow more applied activities. This has most recently occurred
at the University of Leicester with a “Shaping for Excellence" proposal to reduce the size of its Pure Mathe-
matics Group to become teaching only, in order to “meet the rising market demand of artificial intelligence,
computational modelling, digitalisation and data science". The “market demand" vocabulary is of course mis-
leading (they will fail for good reasons – see below) and only present to assure any impartial observers that
the University is being agile, creative, and proactive.
The intellectual argument against this, provided by the LMS [3], rest on assertions such as, “Not only does
the subject form the foundation of many areas of science and technology, its applications to the social sciences
have also been of the highest significance. It has been considered essential in higher education for over 2000 years
and is widely viewed as a pinnacle of human thought. It has never been more prominent in popular intellectual
culture, especially among young people. For a university to cut itself off from this tradition would seem to us to
be a significant step away from what it means to be a seat of academic learning and scholarship, and so to risk
severe reputational damage."
While we accept these LMS points as statements of facts: they do not however represent a strategic case
and they do not raise enough risk — beyond possible reputational damage within a community of global
mathematicians (who willingly sign a petition) and about which the university most likely cares very little at
all.
The problem though is that there are already some mathematics departments which (i) have never had a
significant research activity with pure/fundamental mathematics; or (ii) have persistently reduced or eroded
(run down) their research activities within pure/fundamental mathematics in response to earlier consultations
or performance reviews (in an RAE/REF, for example). Examples of the former and the latter include Brunel
and Reading respectively. These departments invest resources quite heavily in fields of applicable mathemat-
ical sciences. At Brunel the research groupings are Applied and Numerical Analysis, Financial Mathematics
and Operational Research, Statistics and Data Science and Mathematical Physics and Applied Mathematics,
with funded projects involving fundamental mathematics championed by a single member of staff (out of
thirty or so department members). At Reading the research groups cover Applied Statistics; Centre for the
Mathematics of Planet Earth; Complex Fluids and Theoretical Polymer Physics; Data Assimilation and Inverse
Problems; Geophysical Fluid Dynamics; Mathematical Biology; Numerical Analysis and Computational Mod-
elling; Statistical Mechanics, Pure and Applicable Analysis; Number Theory; and Probability and Stochastic
Analysis. Only the latter three contain fundamental elements and these rely on a handful of full-time staff
between them (again out of thirty or so department members). Further examples could be considered. At
Dundee all mathematical research is subdivided into Mathematical Biology, Numerical Analysis and Scientific
Computing, and Magnetohydrodynamics. What ever happened to the fine tradition of Scottish algebra?
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The conclusion is that it is indeed certainly possible to sustain a mathematics department with minimal
or no research within fundamental mathematics, while retaining the desirable elements of teaching the
degree programmes. This rather undermines the above argument that strength in fundamental mathematics
is necessary condition for strength within applications. We have to look further ahead and show how a lack
of such strength will inhibit future applications (see below) and thus the university itself.
However modern exceptions to this “pure and applied growing together" idea stem from the hard fact that
in recent years we have seen a number of topics within fundamental mathematics leap-frog the relatively
traditional applied mathematics topics (fluids, continuum mechanics, mathematical biology, meteorology,
quantitative finance, dynamical systems) and land at the forefront of data science. Computational Topology
(persistent homology) is one such example, where Oxford (and thus the Turing) partnered with niche expertise
at both Swansea and Liverpool. There has also been a massive growth is applied graph (network) theory
over the past two decades, pulled along by a data deluge from social media platforms and application to
marketing, opinion dynamics, public attitudes, hate speech, and much more.
Of course “Shaping" and “Balancing Capabilities" has become standard vocabulary for giving up on any
aim to be casting the research net widely and instead identifying and rewarding some specific priorities at
the expense of other sub-domains. UKRI has been fond of “shaping" in the past. For the EPSRC Mathematical
Sciences programme this means [4]:
•increasing connectedness within the mathematical sciences community by encouraging and supporting
interdisciplinary working;
•supporting and encouraging the development process from fundamental research to user engagement;
•focusing on people and skills, particularly at the early career level.
The second of these is particularly interesting since the above leap-frog fields are exactly what are to be
encouraged, and yet this is ground that some departments may have now ceded. By cleaving to their known
unknowns, within relatively traditional areas of applied mathematics, it is as if they are planning for a refight
of the last war rather than the next one. The folly is in expecting that applied mathematics will continue
as now on a decadal basis and there will not be disruptions that are enabled by fundamental mathematical
breakthroughs. Those are unknown unknowns and the only thing we can know is that they will occur. Get
ready.
We should articulate such expectations and desires in mathematics departments’ strategies – elements
that could not be achieved by shaping fundamental maths, but rather by allowing it to prosper while being
ready to accelerate its connectivity downstream. It is also arguable that the UK will not maintain its interna-
tional; national position of excellence by merely harvesting impact from existing applications (which itself
begets a kind of international arms race), it must pioneer and exploit novel applications based on funda-
mental concepts and ideas. We have recently made a similar case regarding aspirations for AI research [5]
and the limitations induced by a lack of exploration and novelty (from unconventional ideas that may not
get through a consensus-seeking peer review process). The new ARIA is also predicated on this idea [6].
There is a case that might be made that departments that are running down, or closing down, fundamental
mathematical research are doing precisely the wrong thing today, and they should instead be prioritising
fundamental mathematics and aligning themselves with UKRI and the future economic benefits of the UK.
To do so would ensure their future: instead they are walking away.
Indeed the role of public funding and university shaping should be to invest into early stage develop-
ment and innovation that public institutions, companies and venture funds cannot easily justify to their own
funders, investors, stakeholders or shareholders: if they could then they would. This barrier may be because
the activities and outcomes are highly uncertain or high risk, or involve fundamental science (and thus are
long-term), or are open-ended, or require momentum within multidisciplinary fields, or need a diverse range
of talents to which the funder of investor does not have easy access.
So EPSRC has indeed already seen this, and the need to enable such leaps from “fundamental research
to user engagement", while some universities have not. This narrative is far more precise that the special
pleading over the general balance, or the “tending the roots" argument given above, since, although they
seem similar, we can now focuses on processes that make such leaps happen more often, more widely, more
effectively, and more efficiently. And of course departments with a low, or no, amount of fundamental math-
ematics will be excluded from this developing future, that is itself strategically supported by EPSRC/UKRI’s
national strategy.
For some departments that are focussed on growing their existing strategic partnerships within some
specific applied fields, requiring partnerships with external stakeholders and/or other academic departments,
this may not matter so much. But for departments aiming to meet the rising market demand of artificial
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intelligence, computational modelling, digitalisation and data science, this looks like folly. They will be
directly competing against other departments and institutes (such as Turing) where leaps and conbsequent
disruptions are clearly possible. To win within those fields, to disrupt within those fields, will require the
development of ground-breaking fundamental concepts.
At the time of writing, as Leicester’s “Shaping for Excellence" changes are commencing following a con-
sultation (https://le.ac.uk/news/2021/may/shaping-for-excellence-outcomes), it is difficult to en-
vision a U-turn but we should be clear that their strategy for pure mathematics represents a fundamental
misunderstanding of the nature of the domain that they are entering, and the ones they are casting away
instead of boosting. They have given up their ability to innovate and to lead in refreshing their targeted
applied disciplines.
5 Strategic Options for Mathematics Departments
In this section we wish to build up some options for departments to consider when creating a research
strategy, or contributing to others’ strategy (within the faculty, for example). Whether the department is
large or small there are common challenges, aspirations and elements.
5.1 People – growing the intellectual authority
The researchers in the department represent an investment. What can mathematics department members
do together that will build authority with mathematical communities and be extolled and envied by other
universities (a good measure of success)? A department’s strategy should consider what type of future leaders
will be required, within which priority fields, and where they will come from. Can they be grown? Or must
they be recruited? Or both. The diagnosis here should be that research (sub-)fields are changing, perhaps
with very recent disruptive concepts and consequent results, or by new national needs. The policy should be
that the department wishes become more prominent in some of these new directions, which will contribute
to the university’s own strategy and standing. To do so they must nucleate new teams around new leaders,
that will be authoritative and/or fundable. And possibly impactful in a number of ways.
5.1.1 People – growing leaders for the future
Most funders have a programme to support ECRs including various types of fellowship. Increasingly panels
look beyond the technical abilities and achievements and they enquire how a prospective fellow may develop
as a leader. Who would they lead? First, they should be able to lead PDRAs and post grads within their own
team/group (often called a “lab" these days – why?). Second, they should provide evidence that there are
similar researchers across the UK, a community working in similar fields and that this can be drawn together
to create mutual support, competition, tension, and the sharing of ideas - tension and competition are great
drivers in science (both fundamental and applied). That community requires a different type of leadership
where one had no power to compel (influencing sideways), but this is particular natural within mathematics
where ideas are our currency. Third, they should have an ambition to lead an internal initiative within the
department, perhaps supported by the faculty or university. This gives the university an “option" while it
allows the prospective fellow to say clearly how their research objectives align with the strategy of the
faculty. Note that leadership is distinct from doing leading research [2].
For medium (middle) stage career researchers, the departments should assist them with internal or ex-
ternal courses on leadership. Mathematical research leadership is not like normal institutional or corporate
leadership. Essentially mathematics is a creative activity, and research leaders need to be open to ideas and
create a flat interactive structure. It is always good to ask people how they feel about their research direction,
achievements and difficulties, and those of others in the group, in an open and non-judgmental fashion. This
sends out many good signals [2]. Departments should also encourage mid-stage researchers to take on roles
with the professional and learned societies as well as within the research funder ecosystem. This encourages
them to develop a generalist view of mathematics and many related sciences (and to see ourselves as others
see us).
Existing strong research leaders are an asset to a department. However, they should have a clear vision.
How might their research be better supported by the department or university? What aspirations are un-
fulfilled? What opportunities do they foresee in their field? Here we should invite people to look say five
years ahead within their own research field. Many existing leaders will simply say they need to be given time
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and space and allowed to carry on as now. This is a safe answer, yet it makes no case for support. Within
some fields do nothing is the right thing for now. In others it may represent a complete lack of ambition and
vision at best, or clinging on at worst. The mathematics departments should take a dim view of this, and also
encourage researchers to become ambitions.
5.1.2 People – star recruitment
There are two types of opportunity to recruit senior stars: those where a space has been cerated by the
retirement or departure of a staff member; and those where a new role has been created as part of a strategic
push by the university or faculty.
In the latter case the department will have had to argue for such internal investment by articulating a
logic behind a certain type of appointment. This is straightforward within applied and multidisciplinary roles,
when the research might support a pan-university push into these (such as data science, systems biology, AI,
human behaviour/society, or low carbon energy, and so on). It is far less so for fundamental research. In
that case the department should make a case based on how some future research strength within a suitable
fundamental field will refresh the intellectual life of not just the department’s own members, or the university,
but of the nation. The aspiration should be clearly set out in terms of building links to other mathematicians
(key individual and groups in other institutions), some commitment to novel opportunities to provide national
and international leadership (which will see the department rise within, say, the Shanghai league tables),
and the development of more highly ranked research outputs. The case should include the identification of
potential competitors and collaborators (groups within mathematics departments at other universities).
Standing in the shoes of the PVC for research or the Dean, you might feel that the mathematics de-
partment always goes through the motions and makes the case to be part of strategic initiatives, but then
tends to subvert the funds (mathematicians panic and support excellence) and appoint somebody with a
strong research record who is not necessarily fully committed to the underlying corporate initiative. To avoid
this impasse many universities now have initiatives that appoint centrally before placing new hires into the
departments. Exeter pionered this.
The rubric of any strategic funding initiative within universities will usual preclude departments from
just carrying on as now and receiving internal monies for PDRAs, etc. Instead they ask what can be achieved
with the new investment that could not have been achieved otherwise.
5.2 Setting priorities: robbing Peter to pay Paul
What happens when a mathematics department or university seeks to prosper by reducing heads within one
research field in order to recycle that money to invest into others? We have discussed some examples of
this where for various reasons we have seen departments run-down fundamental mathematics with the aim
of recycling monies as overheads to support growth within other fields. There are cases where the other
research fields lie within mathematics (as at Leicester), and also cases where they are completely unrelated,
with the shaping imposed by the university itself (as at Dundee mathematics department, some years ago).
Clearly both types of act are possible, but when are they desirable?
The main point from the discussion in section 4 is that fundamental mathematics can sometimes be
a sitting duck in the cross hairs of larger strategic initiatives. It would be so because it had asserted no
strategic aims (and thus consequent benefits for the host). What does a department or faculty or university
lose if any field of mathematical research is closed down or run down (sun-setted)? A departmental, or
even research group, strategy should be progressive, yet often long-term, and make any risk and loss from
de-prioritisation very specific and very clear. Special pleading and generalisations should be avoided (they
infuriate generalists) in favour of specific aims and targets (policies and some measurable aims). Even the
most long-term and fundamental sub-fields might find alignment with national needs (as represented by
the strategies of research councils or UKRI), and all fields of mathematics should surely have a strategy for
building reputation, authority and excellence (even with their existing heads).
It has to be said that only very rarely have we sat through any conversations about strategy with colleagues
within mathematics research groups: but for senior management this is a large part of their activity and
thinking. Why is there such an obvious disconnect? On visits we sometimes ask research groups what they
are trying to achieve together that will outlast the benefits to the individuals. This is to invite some long
term vision and achievable clear benefit to the host university.
Before robbing one sub-field of research (Peter) to re-invest those resources and grow another (Paul) we
would wish to be assured of the truth (or otherwise) of the following propositions.
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a) Peter is highly unlikely to contribute to any major novel achievements within mathematics: it is past
its prime or the field is diminishing nationally and/or internationally.
b) Peter is rated as a low priority by external funders (EPSRC, Royal Society), learned societies (who often
struggle with priority-setting admittedly) and in International Reviews.
c) There are no implications for other sub-fields of mathematical research arising from losing Peter (Pe-
ter has become independent).
d) There is no demand for graduate courses or PhDs within Peter.
We could invent other criteria. But the point is that we need some assurance that no upside is being lost and
that there will be no collateral damage to the departmental research.
Of course a failure of affected departmental members to engage with, and especially to articulate, re-
search priorities and goals is a very bad sign. Departmental research directors should take a view of the
motivations of those involved and whether their game can ever be improved. After all this is public money
(in a large sense) and universities have a duty to avoid waste.
Note that not one of the above points are about Paul. It is Peter’s relative weaknesses and “nothing to
be lost" attribute that ought to be the primary issue. If all the above propositions are true then perhaps a
responsible department should indeed consider some shaping. Is Paul a good candidate?
Of course we have made the case in section 4 that very often fundamental research provides a game-
changing opportunity both in mathematics and within applications. If any such possibilities occur then that
would be great: yet these “leaps" are rarely, if ever, foreseen. Hence we have to find ways to make this
possibility real and credible within our strategy, and some of the thinking and language above may be useful.
Why are some branches of fundamental mathematics game-changers for mathematics? What would be the
reputational and actionable gains for the university, if successful?
Next we must disconnect the strategy for change from the choice of process/mechanism. Having iden-
tified a possible need to rob Peter (to pay some Paul or other), how will Peter’s be actively be run down, or
closed down? We have seen examples of whole hard science (Mathematics, Physics and Chemistry) depart-
ments close in response to external reviews or else internal priorities to support other departments that need
overheads (perhaps they are heavily funded by the Wellcome Trust without overheads), or with internal funds
for new heads. At its starkest some areas such as fundamental maths may become teaching only (as they are
in other universities already, for different reasons), and there could be redundancies for those research active
staff no-longer required. Such a process follows a strict pattern with the result that the more excellent mem-
bers of staff may seek to jump before they are pushed. In any sector of employment it is always regrettable
to see people leave through redundancies: they have done nothing wrong yet they are now deemed to be not
required. We have seen instances where individuals took a very sever personal toll in such circumstances.
Of course if carrying on was a viable option then that strategic case should have been made long before
the decision came. Voluntary redundancy schemes should be preposed and the LMS and the unions should
support this option as their red line.
5.3 Open innovation networks
A department may adopt policies that build deeper and longer lasting relationships with external stake-
holders and users of all types. In particular they should aspire to being “partners of choice" while providing
upstream knowledge and experience that such partners need but cannot create themselves or in many cases
even justify to their own shareholders or funders. The nation (BEIS) is concerned with the flow of discovery
and innovation from basic science out to support societal and economic benefits.
Departments should also forge relationships with sectors and companies that are large employers of
mathematicians and are also users and deployers of mathematical research. If in doubt follow the alumni.
This requires some proper effort. Universities take more notice of external voices that sumarise the value
of departments than they do of internal claims,
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5.4 International research networks
In mathematical research this includes the development of reputation and international standing, that will
be actionable for the UK via diplomacy through science initiatives with allies and emerging nations. Hence
international partnership with distinct types of countries (at various stages of economic and scientific de-
velopment) are extremely desirable for the UK. Why do mathematics departments not have international
partnering strategies? To be clear this is not about developing foreign campuses, but about building gener-
ational collaborations that can be supported within both countries.
5.5 Establishing a visitor and exchange programme
One way to encourage networking of department members across national and international research groups
is to enable visitors and exchanges. The aim should be to establish interactions between department mem-
bers and authoritative research leaders elsewhere with the aim of creating collaborative research outputs
and forward-looking reviews articulating challenges. While such interactions can occur organically, a formal
regularised reserach exchange programme can be a significant benefit to the departmental researchers and
can seek to place the department at the forefront of appropriate fields.
5.6 Aligning mathematics departments with national strategies – or not
The learned societies are very poor at setting priorities in mathematics: this is because of the diverse interests
of their membership, and priorities imply that if there are winners then there will be losers. The peril of
inclusivity is the enemy of strategy. Conversely, priority setting and shaping have rightly been exploited by
EPSRC for two decades in allocating public money, and consequently almost all universities have followed
suit.
Second-guessing future calls from UKRI can be smart for some universities, and even mathematics de-
partments, if they are suitable and there is ample time to see such things coming. This is especially important
for multi-university mathematical collaborations. For example, if there is a suitable specific call coming in
a years time, then collaborating researchers should discuss their joint potential responses early, they should
publish some forward-looking papers together, and they should build a clear and referenceable track-record
of working together, by holding joint seminars on suitable topcs, and so on. Hence building the team.
We think that mathematics departments should always be well informed about funders’ thinking: public
and charitable. Some opportunities are predictable or annual (for fellowships and so on), while we are now
seeing some very large one-off amounts of funding available for specific thematic opportunities at short
notice. Departments should consult directly with the funders over the possibility for mathematics-centric
bids. Very often funders will welcome this. And an early "no" is useful.
There are some research fields that are within basic research and thus can never be parcelled into thematic
calls. Funders acknowledge this. These fit into responsive mode and various specific schemes (by mechanism
rather than field: grant size and scheme purpose).
We are suggesting that a department’s research strategy should signal the particular types and objectives
of possible calls to which they would respond most competitively, and include the “why" and “what". It should
highlight preparatory steps (building up collaborations and so on). This type of directional information is very
useful for funders. Communicate it.
However we are equally not suggesting that a department’s strategy should be dominated by chasing lots
of funding opportunities. If a call is suitable, then good. But the purpose of the research strategy should
be argue for policies and consequent activities that will chime with a number of interests outside of the
department: and perhaps the most important of these is the host university’s senior management.
Most universities and research funders have public strategies, and hence priorities. Mathematics depart-
ments could align with those that are suitable. But where they are misaligned they should consider why.
Mathematics is special, given its fundamental role within science, its long-term goals, its rigour, and its
community: it is simply not able to align with every novel initiative.
5.7 Research group strategies
Most departments subdivide their research activities into research groups, with regular meetings, specific
seminar series, and some organisational framework for dealing with post graduate applications and so on.
We suggest that each research group should articulate its own vision as a standing item at meetings. There
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Grindrod - Research Strategy for Mathematics Departments
should be a living document that sets out aspirations and expectations of various research directions and
research outputs.
At one university we found it very productive to visit separate research groups across many departments
and ask them what they would wish to do if they had £1M or £5M to invest in their research activities. What
opportunities might they pursue? What would be needed for success? What mechanisms would they wish
adopt? How would they deploy such investment? What would success look like? How soon?
This forward-looking (even horizon scanning) activity quite often turned up some surprising common
causes. In each case they should address some push-back points. Why now? What makes this a realistic
opportunity? Who would be their competitor groups or collaborator groups (eslewhere in the UK or abroad)
under such an initiative?
These are all options and can contribute (or not) to the development of departmental research strategies.
5.8 Research directors and research committees
One of the responsibilities of departmental research director and of members of the departmental research
committee (if there is one) is to support department members in their research career aspirations. Support,
not thwart: enable not disable. Having a few members of the department step forward and offer to be cham-
pions within a research initiative is a very fine thing, since nothing ever happens just because a committee
thinks it is a good idea. Instead we need firm commitment from a champion, one who will enthusiastically
invest time and intellectual effort in making something happen.
Instead many departmental research directors and committees spend most of their time spreading out
resources and opportunities (across the departmental research groups, for example) and act as both decision
makers and a means arbitration. This is useful, but we stress that is only half of the job. Their support for de-
partmental members in formulating initiatives and strategic opportunities is arguably of higher importance,
yet is often deferred (until when?) in favour of the sharing out responsibility.
Some of the most effective mathematicians prefer to just get things done, saying, “It is better to ask for
forgiveness than permission". This happens because departments, faculties, and whole universities are run by
invoking precedents almost all of the times, as their administrators are very wary of creating new precedents
that they might possibly be blamed for later. Consequently there is much process drag and inertia at work,
much conservatism, and this can kill ideas or wear down enthusiasm. It should be the task of the research
director and of members of the departmental research committee to use their antennae and know-how to
help department members avoid such impediments. This is meta strategy: having some assistive support so
that strategic options and initiatives for the future research can be developed by departmental champions.
6 Conclusions
We have introduced a general definition and framework for developing a strategy. We have focussed on
research strategy here, and we have discussed a number of difficulties faced by mathematics departments in
formulating one. We consider strategy to be essential as both a shield and proactive enabler. We have also
discussed various elements that could be part of a mathematics department’s research strategy..
Many readers will think these ideas obvious, yet practices do not often live up to them.
Over the next few years there may be many changes in the ways that universities operate. There will
be changes in how they are funded by government, how research funding is allocated, and the R&D and
innovation ecosystems that operate in post-Brexit UK. We are seeing national strategies imposed via UKRI
and the nascent ARIA. Some universities may go bust. Now is not a time to be naked, to be without a strategy.
Strategy will give us something to push against, some anchors. Strategising should also create a common
cause, sharing what works across the whole UK mathematics community, between all of the departments of
mathematics.
A mathematics department might contribute in many ways to the development of strategies for their host
universities. But first it should set its own house in order.
References
[1] R. Rumelt (2011), Good Strategy/Bad Strategy: The Difference and Why it Matters, New York: Crown
Business
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Grindrod - Research Strategy for Mathematics Departments
[2] P. Grindrod (2020), Leading Within Digital Worlds, Emerald Publishing Limited.
[3] London Mathematical Society (2021), Mathematics at the University of Leicester, https://www.lms.
ac.uk/news-entry/09022021-1444/mathematics-university-leicester.
[4] EPSRC, Mathematical Scinces Programme, Theme strategy in relation to Balancing Capability, https:
//epsrc.ukri.org/research/ourportfolio/themes/mathematics/ourapproach/.
[5] P. Grindrod (2021), Unconventional AI, ReserachGate https://www.researchgate.net/publication/
351840329_Unconventional_AI.
[6] HM Government, BEIS (2021), Advanced Research and Invention Agency (ARIA): policy statement,
https://tinyurl.com/vbppxbpa.
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